IJE TRANSACTIONS A: Basics Vol. 31, No. 7 (July 2018) 1109-1116    Article in Press

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M. Dehghani
( Received: November 23, 2017 – Accepted in Revised Form: January 16, 2018 )

Abstract    In this paper a general analytical solution is obtained to find stress distribution in a finite elastic plate with a circular or square hole subjected to arbitrary biaxial partial loading using modified boundary condition by assuming plane stress conditions. The method employed is based on solution of circular hole in finite rectangular plate. This plate is mapped to circular ones and the partial loading is transformed to new boundaries as form of triangular functions. The Airy stress functions are selected according to these triangular functions and the unknown factors of Airy stress functions are derived by applying boundary conditions. The stresses in this plate with circular hole are mapped to plate with square hole using Muskhelishvili’s complex variable method. The results of this method are compared with theoretical solution of infinite plate and finite elemnt method solution of finite plate. The results showed the dimensions of plate and square hole and length of biaxial partial loading affected on Von Mises stress around the square hole. Von Mises stress increases around the square hole by decreasing length of the plate or increasing hole’s area.


Keywords    Square Hole; Finite Plate; Partial Biaxial Loading; Complex Variable Method


چکیده    در این مقاله تنش اطراف سوراخ مربع شکل در ورق با اندازه محدود تحت بار مکانیکی پاره‌ای در راستای طول و عرض این ورق با تغییر مرزهای ورق مستطیلی به منحنی شکل و فرض تنش صفحه ای به روش تحلیلی بررسی شد‌ه‌است. در روش به‌کاررفته، از حل صفحه محدود با سوراخ دایره‌ای در مرکز آن به عنوان مرجع استفاده‌شده است. مرزهای قائم ورق به منحنی تبدیل شده و بار مکانیکی وارده به بخشی یا تمام مرز قائم ورق به شکل توابع مثلثاتی تبدیل گردیده و تابع تنش ایری متناظر با آن انتخاب شده‌است. با اعمال شرایط مرزی، ضرایب مجهول تابع تنش ایری به دست آمده‌اند و تنش‌های اطراف سوراخ دایره‌ای در ورق محدود محاسبه شده‌ است. به کمک روش توابع مختلط، توزیع تنش به دست آمده در این صفحه محدود با سوراخ دایره‌ای به صفحه محدود شامل گشودگی مربعی انتقال یافته است. نتایج حاصل از این روش با حل تئوری ورق با اندازه بینهایت و حل اجزا محدود ورق محدود مقایسه شده است. در قسمت نتایج تأثیر پارامترهای مؤثر بر تنش شامل طول اضلاع ورق، اندازه سوراخ بررسی گردیده و نشان داده شده‌است که با کاهش اندازه ابعاد ورق یا افزایش قطر سوراخ، مقدار ماکسیمم تنش ونمایسز اطراف مرز آن افزایش می‌یابد.


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